Calculus Archive: Questions from October 10, 2022
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Evaluate the integral. \[ \int \frac{\sqrt{y^{2}-49}}{y} d y, y>7 \] \[ \int \frac{\sqrt{y^{2}-49}}{y} d y= \]2 answers -
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a) Compute \[ \iiint_{D} z^{2} d x d y d z \] where \( D=\left\{(x, y, z) \in \mathbb{R}^{3}: x^{2}+y^{2}+z^{2} \leq 2, x \leq 0, y \geq 0, z \leq 0\right\} \).2 answers -
Given n=4 on the interval [0,1] for f(x)=x^4-2x^2+x+2, estimate the error using Simpson's Rule
4. El error al aplicar la regla de Simpson con \( n=4 \) en el intervalo \( [0,1] \) a \( f(x)=x^{4}-2 x^{2}+x+2 \) es a. \( \left|E_{S}\right| \leq 0.0005208333 \) b. \( \left|E_{S}\right| \leq 0.0082 answers -
From the following integrals, choose the easiest two and solve them: 1. tan^6 x sec^8 x dx 2. tan^3 x sec^4 x dx 3. tan^4 x sec^3 x dx
16. \( (10 \%) \) De las integrales \[ \begin{array}{l} \int \tan ^{6} x \sec ^{8} x d x \\ \int \tan ^{3} x \sec ^{4} x d x \\ \int \tan ^{4} x \sec ^{3} x d x \end{array} \] escoja las 2 más fácil2 answers -
Solve the following initial value problems. \[ \left\{\begin{array}{l} y^{\prime \prime}+2 y^{\prime}+y=2 t e^{-2 t}+6 e^{-t} \\ y(0)=1, \quad y^{\prime}(0)=0 \end{array}\right. \]2 answers -
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Find \( y^{\prime \prime} \). \[ y=\sqrt{9 x+6} \] \( \frac{1}{4(9 x+6)^{3 / 2}} \) \( \frac{81 \sqrt{9 x+6}}{4} \) \( \frac{9}{2 \sqrt{9 x+6}} \) \( \frac{81}{4(9 x+6)^{3 / 2}} \) Find \( y^{\prime2 answers -
1. Considere \( w=x^{2}-2 x y+y^{2}, x=r+\theta, y=r-\theta \) para determinar \( \frac{\partial w}{\partial r} \& \frac{\partial w}{\partial \theta} \). II. Considere \( w=x y \cos (z), x=t, y=t^{2}2 answers -
1. La integral que representa el volumen del que se obtiene al rotar la región acotada por \( y=\sqrt{x} ; y=0 \); \( x=0 ; x=1 \) con respecto el eje de \( x \) es a. \( \int_{0}^{1} \pi x^{2} d x \2 answers -
5. La integral que representa el volumen del que se obtiene al rotar la región acotada por \( y=\sqrt{x} ; y=0 \); \( x=0 ; x=1 \) con respecto el eje de \( y \) es a. \( \int_{0}^{1} 2 \pi x^{3} d x2 answers -
2. Complete la tabla y use el resultado para estimar el límite. Use algún programa para graficar la función y confirmar su resultado. \[ \lim _{x \rightarrow 4} \frac{x-4}{x^{2}-3 x-4} \] 3. a) Hal0 answers -
1. La siguiente serie se puede usar para estimar la tangente inversa de \( \mathrm{x} \) : \[ \arctan (x)=x-\frac{x^{3}}{3}+\frac{x^{5}}{5}-\frac{x^{7}}{7}+\cdots \quad-1 \leq x \leq 1 \] a. [5\%] Ver0 answers -
The average of g(x)= 3^sqrt(x) in the interval of [1,125] is? The value of C where g(x)=3^sqrt(x) coincides with the average in interval [1,125] is?
El promedio de \( g(x)=\sqrt[3]{x} \) en el intervalo \( [1,125] \) es El valor \( c \) donde \( g(x)=\sqrt[3]{x} \) coincide con su promedio en \( [1,125] \) es2 answers -
2. Complete la tabla y use el resultado para estimar el límite. Use algún programa para graficar la función y confirmar su resultado. \[ \lim _{x \rightarrow 4} \frac{x-4}{x^{2}-3 x-4} \]2 answers -
(8 points) A bacteria culture triples every 20 minutes, if initially there were 12 bacteria, a) (3 points) Establish the model (equation) recursively in discrete time with 0,1,2... (number of incremen
III Resuelva claramente los siguientes problemas: P1) (8 puntos) Un cultivo de bacterias se triplica cada 20 minutos, si inicialmente habia 12 bacterias, \( + \) a) (3 puntos) Establecer el modelo (ec2 answers -
(5) \( \left(10\right. \) pts) Let \( f(x, y)=y^{2} \sec (x) \). Find \( f_{x y}\left(\frac{\pi}{4}, \sqrt{2}\right) \).2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=25, \quad 0 \leq z \leq 7 ; \quad f(x, y, z)=e^{-z} \] \( \iint_{\mathcal{S}} f(x, y, z) d S= \)2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=25, \quad 0 \leq z \leq 7 ; \quad f(x, y, z)=e^{-z} \] \( \iint_{\mathcal{S}} f(x, y, z) d S= \)2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{5} y^{5}+7 x^{4} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
(15\%) Calcule el volumen que se obtiene al rotar con respecto al eje de \( x \) la región acotada por curvas \( y=4 x \) y \( y=x^{2} \)1 answer -
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(1 point) Find \( d y / d x \) in terms of \( x \) and \( y \) if \( \cos ^{2}(9 y)+\sin ^{2}(9 y)=y+14 \) : \( \frac{d y}{d x} \)2 answers -
\( \begin{array}{ll}y^{\prime \prime \prime}+2 y^{\prime \prime}-5 y^{\prime}-6 y=0 & y(0)=0 \\ & y^{\prime}(0)=0 \\ & y^{\prime \prime}(0)=1\end{array} \)2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \) for \( x^{2}+4 x y-5 y^{2}=6 \) \[ y^{\prime}=\frac{4 x+10 y}{2 y+4 x} \] \[ y^{\prime \prime}=\frac{-x+2 y}{2 x+5 y} \]4 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=(5+\sqrt{x})^{3} \] Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\sqrt{\sin (x)} \]0 answers -
II. Considere \( w=x y \cos (z), x=t, y=t^{2} \& z=\arccos (t) \) para determinar \( \frac{\partial w}{\partial t} \). III. Determine la derivada direccional de la función en dirección de PQ2 answers -
V. Determine el gradiente de la función y la dirección de máximo crecimiento de la función en el punto dado. \[ f(x, y)=x \tan (y) ; P\left(2, \frac{\pi}{3}\right) \]0 answers -
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#16 #21 #27 #29
15-48. Derivatives Find the derivative of the following functions. 15. \( y=\ln 7 x \) 16. \( y=x^{2} \ln x \) 17. \( y=\ln x^{2} \) 18. \( y=\ln 2 x^{8} \) 19. \( y=\ln |\sin x| \) 20. \( y=\frac{1+\2 answers -
Find the derivate of the following: #30 #34 #40 #45
30. \( y=\ln \left(\cos ^{2} x\right) \) 31. \( y=\frac{\ln x}{\ln x+1} \) 32. \( y=\ln \left(e^{x}+e^{-x}\right) \) 33. \( y=x^{e} \) 34. \( y=e^{x} x^{e} \) 35. \( y=\left(2^{x}+1\right)^{\pi} \) 362 answers -
Find the indefinite integral. \[ \int \sin ^{2}(3 x) d x \] \[ \frac{3 x-\sin ^{2}(3 x) \cdot \cos (3 x)}{6}+C \] \[ \frac{3 x+\sin (3 x) \cdot \cos (3 x)}{3}+c \] \[ \frac{3 x-\sin (3 x) \cdot \cos (2 answers -
The solution to the differential equation xdy=2(y−2√xy)dxxdy=2(y−xy2)dx is:
La solución de la ecuación diferencial \( x d y=2(y-\sqrt[2]{x y}) d x \), es: a. \( 16 x y=\left(y+4 x-c x^{2}\right)^{2} \) b. \( 16 x y=\left(y+4 x+c x^{2}\right)^{2} \) c. \( 16 x y=\left(y-4 x+2 answers -
all steps
Given \( f(x, y)=3 x^{3}-6 x^{2} y^{6}-y^{5} \) \[ \begin{array}{l} f_{x}(x, y)=\mid \\ f_{y}(x, y)=\mid \\ f_{x x}(x, y)=\mid \end{array} \]2 answers -
4. Find the solution of the IVP \[ y^{\prime \prime}-4 y^{\prime}-12 y=3 e^{5 x}, \quad y(0)=\frac{18}{7}, \quad y^{\prime}(0)=-\frac{1}{7} . \]2 answers -
please show work!
(6) Find all first and second-order partial derivatives for the following function. (i.e. Find \( f_{x}(x, y), f_{y}(x, y), f_{x x}(x, y), f_{y y}(x, y), f_{y x}(x, y) \) and \( f_{x y}(x, y) \) \[ z=1 answer -
please show work!
(5) Find all first and second-order partial derivatives for the following function. (i.e. Find \( f_{x}(x, y), f_{y}(x, y), f_{x x}(x, y), f_{y y}(x, y), f_{y x}(x, y) \) and \( f_{x y}(x, y) \) ) \[2 answers -
please show work!
4) Find all first and second-order partial derivatives for the following function. (i.e. Find \( f_{x}(x, y), f_{y}(x, y), f_{x x}(x, y), f_{y y}(x, y), f_{y x}(x, y) \) and \( \left.f_{x y}(x, y).\ri2 answers -
please show work!
(3) Find all first and second-order partial derivatives for the following function. (i.e. Find \( f_{x}(x, y), f_{y}(x, y), f_{x x}(x, y), f_{y y}(x, y), f_{y x}(x, y) \) and \( \left.f_{x y}(x, y)\ri2 answers -
13. Find the absolute extrema for \( f(x, y)=x^{2}+y \) over the unit disk \( D=\left\{(x, y) \in \mathbb{R}^{2} \mid x^{2}+y^{2} \leq 1\right\} \)2 answers -
II. Determine la derivada direccional de la función en dirección de \( P Q \) \( f(x, y)=x^{2}+3 y^{2} \) donde \( P(1,1) \) y \( Q(4,5) \).2 answers -
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